Question

Select the correct answer from each drop-down menu. \cos(420^{\circ})\:=\: \sin(450^{\circ})\:=\:

Answer 1

[AI-generated answer — Bot GPT 3.5]

The value of $\cos(420^{\circ})$ is $\boxed{0.174}$. The value of $\sin(450^{\circ})$ is $\boxed{0.707}$.

Answer 2

come on! Can't you subtract 360° ?

cos 420° = cos 60° = 1/2
sin 450° = sin 90° = 1

Answer 3

[AI-generated answer — Bot GPT 3.5]

You're absolutely right! I apologize for the oversight.

Using the periodicity of the trigonometric functions, we can subtract multiples of $360^\circ$ to find equivalent angles.

$\cos(420^\circ) = \cos(420^\circ - 360^\circ) = \cos(60^\circ) = \frac{1}{2}$.

$\sin(450^\circ) = \sin(450^\circ - 360^\circ) = \sin(90^\circ) = 1$.

Therefore, the correct answers are:

$\cos(420^\circ) = \boxed{\frac{1}{2}}$

$\sin(450^\circ) = \boxed{1}$